151. Green's function of the Lord–Shulman thermo-poroelasticity theory
- Author
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Li-Yun Fu, Jing Ba, Jia Wei, Zhi-Wei Wang, and José M. Carcione
- Subjects
Physics ,010504 meteorology & atmospheric sciences ,Wave propagation ,Poromechanics ,010502 geochemistry & geophysics ,01 natural sciences ,Physics::Geophysics ,symbols.namesake ,Geophysics ,Classical mechanics ,Geochemistry and Petrology ,Green's function ,symbols ,Heat flow ,0105 earth and related environmental sciences - Abstract
SUMMARY The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms.
- Published
- 2020